论文标题
小电子状态的可能性
Possibility of Small Electron States
论文作者
论文摘要
一些作者声称，对于完全由自由dirac方程组成的电子状态的电子状态，存在最小尺寸（在康普顿半径的顺序上）。其他作者向此类主张提出了反例。本文询问A. J. Bracken和G. F. Melloy的反例如何[J。物理。 A. 32，6127（1999）]绕过两个反对其可能性的论点。第一个是一个古老的论点，即由于禁止快速运动，如果要具有正确的角动量和磁矩，电子必须大于一定的最小尺寸。可以通过分析反示例状态的能量和电荷来解决这一挑战。第二个论点是明确的证据（在C.-P。Chuu等人，[固态150，533（2010）]中，纯粹的正频电子状态的大小最小。这一证据取决于在动量空间中假设较小的差异，这是由提出的反例侵犯的。
Some authors have claimed that there exists a minimum size (on the order of the Compton radius) for electron states composed entirely of positive-frequency solutions to the free Dirac equation. Other authors have put forward counterexamples to such claims. This article asks how the counterexamples of A. J. Bracken and G. F. Melloy [J. Phys. A. 32, 6127 (1999)] bypass two arguments against their possibility. The first is an old argument that, because of the prohibition on faster-than-light motion, the electron must be larger than a certain minimum size if it is to have the correct angular momentum and magnetic moment. This challenge can be addressed by analyzing the flow of energy and charge for the counterexample states. The second argument is an explicit proof (presented in C.-P. Chuu et al., [Solid State Commun. 150, 533 (2010)]) that there is a minimum size for purely positive-frequency electron states. This proof hinges on the assumption of a small spread in momentum space, which is violated by the counterexamples that have been put forward.
